{
  "id": "1712.09732",
  "version": "v1",
  "published": "2017-12-26T06:43:22.000Z",
  "updated": "2017-12-26T06:43:22.000Z",
  "title": "Characterization of the Two-Dimensional Five-Fold Translative Tiles",
  "authors": [
    "Qi Yang",
    "Chuanming Zong"
  ],
  "comment": "16 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:1711.02514, arXiv:1712.01122",
  "categories": [
    "math.MG"
  ],
  "abstract": "In 1885, Fedorov discovered that a convex domain can form a lattice tiling of the Euclidean plane if and only if it is a parallelogram or a centrally symmetric hexagon. It is known that there is no other convex domain which can form two-, three- or four-fold translative tiling in the Euclidean plane, but there are centrally symmetric convex octagons and decagons which can form five-fold translative tilings. This paper characterizes all the convex domains which can form five-fold translative tilings of the Euclidean plane.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-26T06:43:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C22"
    ],
    "keywords": [
      "two-dimensional five-fold translative tiles",
      "form five-fold translative tilings",
      "euclidean plane",
      "convex domain",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}